Pretty new here so I guess I'll just explain my situation.
I have a 10 week old puppy (miniature dachshund) who has been very good at paper training. He usually defecates/eliminates on the newspaper in a designated spot no matter if we're there or he's left alone. He has a crate but we give him full run of the kitchen (puppy proofed).

He is always playful, energetic and wags his tail whenever someone enters the room, however for the past 2 days when he walks over to the newspaper area to defecate (poop) he will begin and then let out a loud yelp/scream while running and defecating at the same time.

We haven't fed him anything other than kibble and treats: puppy treats (Wellness) and the occasional peanut butter filled kong. (No chicken bones, people scraps, etc) He does defecate sometimes during the day without incident and the other day when taking him for a walk, he pooped out one of the strings on his chew toy (came with 3 strings, took other two, he ate one) but other than that, no toys were broken/damaged.

Not sure what is wrong (he doesn't butt shuffle or whimper when you pick him up) and I get a little worried. We also just had a vet visit for his shots approximately 6 days ago and everything was fine. He also has the occasional hiccup but as I'm a first time dog owner, I want to know if this is normal for puppies?

If it's painful to pass motions only days after a vaccination, then that has to be one of the possible causes, when you have eliminated other more obvious causes. The best people to deal with vaccination problems are holistic vets and homeopaths.
Kibble is not a healthy food for any dog and can create bowel problems. It creates more health problems than any raw bone will ever do.

Don't leave him alone with chew toys, or anything. You would be surprised what puppies can ingest. My Boston is good example of that, still does at 2. I would consider the crate when you are away. Had a dobe eat pantyhose whole and that wasn't easy getting it out. I'm lucky I didn't have to do surgery at the time. Add some canned food and water to the kibble and re-hydrate it for him.

10 weeks is still very young. Has he been checked for worms?
I would not give very many cookies or peanut butter at this age. He needs to grow with a good puppy diet.
As you have discovered, try to give only durable toys like a Nylabone or Kong if you are not around to supervise.
I'm thinking he needs another vet check and poo analysis. Good Luck

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Bina
Please have pets spayed and neutered,
and wearing a collar with an ID tag.

If it's painful to pass motions only days after a vaccination, then that has to be one of the possible causes, when you have eliminated other more obvious causes. The best people to deal with vaccination problems are holistic vets and homeopaths.
Kibble is not a healthy food for any dog and can create bowel problems. It creates more health problems than any raw bone will ever do.

Uhm. I disagree, kibble is healthy for dogs...

I would take puppers to the vet and get him checked out, the answer to your question is no, it is not normal to run and scream while pooping. He could be constipated, or have something serious, who knows, it is worth a check. Good lcuk

I don't suppose it could have been possible that that string toy had more than string in it ?

Besides, you'd be surprised what a dog can get into in the smallest of confined areas. I mentioned in another thread that my dog picked up / ate something that made her sick while she was being watched like a hawk. You'd have to be made of eyes. My dog has been known to bite her toenails, anything I supposed could cause a little wince on the way out.

It's odd though, and I think untypical, for your dog to have that extreme of a reaction to even a sore butt. My dog (after the mysterious edible and resulting sicklies above), was so sore after being sick that she cried and cried while the vet took her temp and checked her butt, but never while she had been pooping. She also once had badly impacted anal glands, with no wince's but butt-scooting ...the wincing and screeching was at the vet . The only time she's ever done the travelling poop parade is if she was really sick, or got a really good scare.

Is his tail ok ? Could the movement req'd to poop be twinging the tail somehow ? No chance anyone walked on his tail by accident ?

poor baby, it's always scary when they do the screech, even when it's at the vet. Can't hurt to do a follow up call to vet to ask for advice, see if this could be a vaccination issue.

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Someday I hope to be the kind of person my dog thinks I am

Not anal fissures is it? Sometimes they do develop in very young pups . But I would have the pup checked before jumping to conclusions, peace of mind being the no. 1 reason. And there just might be something he can't pass. Does he eat grass and could it be too sharp when he passes it?